|June 16th, 2010, 05:57 PM||#1|
Joined: Feb 2009
The range of a matrix transformation
How to do you determine if a vector (w) is in the range a matrix transformation.
Let f: R^2 --> R^3
f(x) = Ax
Why is it a no?
My work: ( I don't know if I'm doing it right)
and why is for Vector w, it's a yes?
The book says that the set of all images of the vectors in R^n is called the range of f. I don't know what it means. Can someone please explain to me how to determine the range. Thanks in advance
|June 16th, 2010, 07:21 PM||#2|
Joined: Oct 2007
Re: The range of a matrix transformation
You want w= f(v) = Av, where v is a vector .
The equation should be:
You cannot substitute values of w into v, you need to see if any value of v, when multiplied by A gives you w. See if there is any v=[x,y] which satisfies this equation.
Edit: Some clarification. "The set of all images" is the set . So, if w is in the image, w=f(v) for some vector v in R^2. To check if such a vector exists, see if there is any vector which satisfies f(v)=w.
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